# Character sums with smooth numbers

## TL;DR

This paper improves bounds on the frequency of large character sums with smooth numbers by leveraging the large sieve inequality for smooth numbers, advancing understanding in analytic number theory.

## Contribution

It introduces improved bounds on character sums with smooth numbers using the large sieve inequality, refining previous results by Drappeau, Granville, and Shao.

## Key findings

- Enhanced bounds on the frequency of large character sums
- Refined estimates for pairs of moduli and primitive characters
- Application of the large sieve inequality to smooth numbers

## Abstract

We use the large sieve inequality for smooth numbers due to S. Drappeau, A. Granville and X. Shao (2017), together with some other arguments, to improve their bounds on the frequency of pairs $(q,\chi)$ of moduli $q$ and primitive characters $\chi$ modulo $q$, for which the corresponding character sums with smooth numbers are large.